The Laplace approach in microrheology.

When coupled with the generalized Stokes-Einstein (GSE) equation, it is often reported that micro-rheology probes the dynamic properties differently than do macroscopic rheological measurements, especially in relatively condensed systems. In the present work, we empirically examine the GSE in its widely used form: following an analytical continuation, the Fourier transformed particle mean-square displacement (MSD) is used to determine the dynamic moduli [G'(ω) and G''(ω)] and we compare the results with those obtained by direct inverse Laplace transform calculation of the relevant viscoelastic functions (either relaxation modulus or creep compliance) from the MSD. The results show that the inverse Laplace approaches can differ from the Fourier approach and give better agreement with macroscopic rheological measurements when this is the case. Some instances of agreement between the Fourier approach and the direct Laplace transform approaches are also shown. It is recommended that micro-rheology MSD data be interpreted using one of the direct Laplace transform based approaches.

"Dense diffusion" in colloidal glasses: short-ranged long-time self-diffusion as a mechanistic model for relaxation dynamics.

Despite decades of exploration of the colloidal glass transition, mechanistic explanation of glassy relaxation processes has remained murky. State-of-the-art theoretical models of the colloidal glass transition such as random first order transition theory, active barrier hopping theory, and non-equilibrium self-consistent generalized Langevin theory assert that relaxation reported at volume fractions above the ideal mode coupling theory prediction φg,MCT requires some sort of activated process, and that cooperative motion plays a central role. However, discrepancies between predicted and measured values of φg and ambiguity in the role of cooperative dynamics persist. Underlying both issues is the challenge of conducting deep concentration quenches without flow and the difficulty in accessing particle-scale dynamics. These two challenges have led to widespread use of fitting methods to identify divergence, but most a priori assume divergent behavior; and without access to detailed particle dynamics, it is challenging to produce evidence of collective dynamics. We address these limitations by conducting dynamic simulations accompanied by experiments to quench a colloidal liquid into the putative glass by triggering an increase in particle size, and thus volume fraction, at constant particle number density. Quenches are performed from the liquid to final volume fractions 0.56 ≤ φ ≤ 0.63. The glass is allowed to age for long times, and relaxation dynamics are monitored throughout the simulation. Overall, correlated motion acts to release dynamics from the glassy plateau - but only over length scales much smaller than a particle size - allowing self-diffusion to re-emerge; self-diffusion then relaxes the glass into an intransient diffusive state, which persists for φ < 0.60. We observe similar relaxation dynamics up to φ = 0.63 before achieving the intransient state. We find that this long-time self-diffusion is short-ranged: analysis of mean-square displacement reveals a glassy cage size a fraction of a particle size that shrinks with quench depth, i.e. increasing volume fraction. Thus the equivalence between cage size and particle size found in the liquid breaks down in the glass, which we confirm by examining the self-intermediate scattering function over a range of wave numbers. The colloidal glass transition can hence be viewed mechanistically as a shift in the long-time self-diffusion from long-ranged to short-ranged exploration of configurations. This shift takes place without diverging dynamics: there is a smooth transition as particle mobility decreases dramatically with concomitant emergence of a dense local configuration space that permits sampling of many configurations via local particle motion.

Physical aging and compressed exponential behaviors in a model soft colloidal system.

Diffusing wave spectroscopy (DWS)-based micro-rheology has been used in different optical geometries (backscattering and transmission) as well as different sample thicknesses in order to probe system dynamics at different length scales [D. J. Pine, D. A. Weitz, J. X. Zhu, E. Herbolzheimer. J. Phys., 1990, 51(18), 2101-2127]. Previous study from this lab [Q. Li, X. Peng, G. B. McKenna. Soft Matter, 2017, 13(7), 1396-1404] indicates the DWS-based micro-rheology observes the system non-equilibrium behaviors differently from macro-rheology. The object of the present work was to further explore the non-equilibrium dynamics and to address the range of utility of DWS as a micro-rheological method. A thermo-sensitive core-shell colloidal system was investigated both during aging and subsequent to aging into a metastable equilibrium state using temperature-jump induced volume fraction-jump experiments. We find that in the non-equilibrium state, significant differences in the measured dynamics are observed for the different geometries and length scales. Compressed exponential relaxations for the autocorrelation function g2(t) were observed for large length scales. However, upon converting the g2(t) data to the mean square displacement (MSD), such differences with length scale diminished and the long-time MSD behavior was consistent with diffusive behavior. These observations in the non-equilibrium behaviors for different length scales leads to questioning of some interpretations in the current field of light scattering-based micro-rheology and provides a possibility to interrogate the aging mechanisms in colloidal glasses from a broader perspective than normally considered in measurements of g2(t) using DWS-based micro-rheology.

Long-term aging behaviors in a model soft colloidal system.

Colloidal and molecular systems share similar behaviors near to the glass transition volume fraction or temperature. Here, aging behaviors after volume fraction up-jump (induced by performing temperature down-jumps) conditions for a PS-PNIPAM/AA soft colloidal system were investigated using light scattering (diffusing wave spectroscopy, DWS). Both aging responses and equilibrium dynamics were investigated. For the aging responses, long-term experiments (100 000 s) were performed, and both equilibrium and non-equilibrium behaviors of the system were obtained. In the equilibrium state, as effective volume fraction increases (or temperature decreases), the colloidal dispersion displays a transition from the liquid to a glassy state. The equilibrium α-relaxation dynamics strongly depend on both the effective volume fraction and the initial mass concentration for the studied colloidal systems. Compared with prior results from our lab [X. Di, X. Peng and G. B. McKenna, J. Chem. Phys., 2014, 140, 054903], the effective volume fractions investigated spanned a wider range, to deeper into the glassy domain. The results show that the α-relaxation time τα of the samples aged into equilibrium deviate from the classical Vogel-Fulcher-Tammann (VFT)-type expectations and the super-Arrhenius signature disappears above the glass transition volume fraction. The non-equilibrium aging response shows that the time for the structural evolution into equilibrium and the α-relaxation time are decoupled. The DWS investigation of the aging behavior after different volume fraction jumps reveals a different non-equilibrium or aging behavior for the considered colloidal systems compared with either molecular glasses or the macroscopic rheology of a similar colloidal dispersions.

Dynamics of a thermo-responsive microgel colloid near to the glass transition.

In a previous study, we used diffusing wave spectroscopy (DWS) to investigate the aging signatures of a thermo-sensitive colloidal glass and compared them with those of molecular glasses from the perspective of the Kovacs temperature-jump, volume recovery experiments [X. Di, K. Z. Win, G. B. McKenna, T. Narita, F. Lequeux, S. R. Pullela, and Z. Cheng, Phys. Rev. Lett. 106, 095701 (2011)]. In order to further look into the glassy behavior of colloidal systems, we have synthesized a new core/shell particle with lower temperature sensitivity and studied the aging signatures of concentrated systems, again following Kovacs' protocol. Similar signatures of aging to those observed previously were seen in this new system. Moreover, a systematic study of the temperature dependence of the dynamics of the new system for different weight concentrations was performed and the dynamic fragility index m was determined. We have also explored the use of the properties determined from the DWS measurements to obtain macroscopic rheological parameters - storage modulus G(')(ω) and loss modulus G(″)(ω) - using a generalized Stokes-Einstein approach. The micro-rheological and macro-rheological values are in reasonable agreement.

Softness mapping of the concentration dependence of the dynamics in model soft colloidal systems.

The dynamics of a series of soft colloids comprised of polystyrene cores with poly(N-isopropylacrylamide) (PNIPAM) coronas was investigated by diffusing wave spectroscopy (DWS). The modulus of the coronas was varied by changing the cross-link density and we were able to interpret the results within a hard-soft mapping framework. The soft, swellable particle properties were modeled using an extended Flory-Rehner theory and a Hertzian pair potential. Following volume fraction jumps, softness effects on the concentration dependence of dynamics were determined, with a 'soft colloids make strong glass-forming liquid'-type of behavior observed close to the nominal glass transition volume fraction, φg. Such behavior from the current systems cannot be fully explained by the osmotic deswelling model alone. However, inspired by the soft-hard mapping from Schmiedeberg et al, [Europhys. Lett. 2011, 96(3), 36010] we estimated effective hard-sphere diameters and achieved a successful mapping of the α-relaxation times to a master curve below φg. Above φg, the curves no longer collapse but show strong deviations from a Vogel-Fulcher type of divergence onto soft jamming plateaux. Our results provide evidence that osmotic deswelling itself cannot fully explain the observed dynamics. Softness also plays an important role in the dynamics of soft, concentrated colloids.

Physical aging and structural recovery in a colloidal glass subjected to volume-fraction jump conditions.

Three important kinetic phenomena have been cataloged by Kovacs in the investigation of molecular glasses during structural recovery or physical aging. These are responses to temperature-jump histories referred to as intrinsic isotherms, asymmetry of approach, and memory effect. Here we use a thermosensitive polystyrene-poly (N-isopropylacrylamide)-poly (acrylic acid) core-shell particle-based dispersion as a colloidal model and by working at a constant number concentration of particles we use temperature changes to create volume-fraction changes. This imposes conditions similar to those defined by Kovacs on the colloidal system. We use creep experiments to probe the physical aging and structural recovery behavior of colloidal glasses in the Kovacs-type histories and compare the results with those seen in molecular glasses. We find that there are similarities in aging dynamics between molecular glasses and colloidal glasses, but differences also persist. For the intrinsic isotherms, the times t_{eq} needed for relaxing or evolving into the equilibrium (or stationary) state are relatively insensitive to the volume fraction and the values of t_{eq} are longer than the α-relaxation time τ_{α} at the same volume fraction. On the other hand, both of these times grow at least exponentially with decreasing temperature in molecular glasses. For the asymmetry of approach, similar nonlinear behavior is observed for both colloidal and molecular glasses. However, the equilibration time t_{eq} is the same for both volume-fraction up-jump and down-jump experiments, different from the finding in molecular glasses that it takes longer for the structure to evolve into equilibrium for the temperature up-jump condition than for the temperature down-jump condition. For the two-step volume-fraction jumps, a memory response is observed that is different from observations of structural recovery in two-step temperature histories in molecular glasses. The concentration dependence of the dynamics of the colloidal dispersions is also examined in the equilibrium state and we find that the dynamic fragility index m is sensitive to the degree of softness of the soft colloidal dispersion, indicating that soft colloids make stronger glasses. Finally, we compare the present results with prior findings for similar thermoresponsive systems obtained with diffusing wave spectroscopy and discuss similarities and differences.

High-performance liquid chromatography coupled with mass spectrometry for analysis of ultrasmall palladium nanoparticles.

Metal nanoparticles (NPs) have recently attracted considerable attention in many areas of research including bioscience, chemistry and material science. Regrettably, most current and past work usually focuses on studies of multi-component NPs mixture where there is a plethora of NPs species co-existing. This work highlights the merits of reverse-phase high-performance liquid chromatography (RP-HPLC) for disclosing the genuine properties of individual palladium nanoparticles (PdNPs) species present in an as-synthesized N,N'-dimethylformamide-stabilized PdNPs product (DMF-PdNPs) which might have been previously hidden or misinterpreted. DMF-PdNPs is successfully separated by RP-HPLC that smaller DMF-PdNPs are approximately eluted first and then follow by the large ones on a C18 column. The separation fractions are further collected and determined their chemical compositions by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry. The results unambiguously reveal that the as-synthesized DMF-PdNPs product is indeed a complex mixture of ultrasmall PdxNPs (x=10-20) stabilized with different numbers of DMF ligands. It is anticipated that the separated fractions afforded by RP-HPLC will offer more accurate determinations of the catalytic, electronic, optical and toxicological properties of metal NPs which might have been previously misinterpreted.

Comparison of the physical aging behavior of a colloidal glass after shear melting and concentration jumps.

Colloidal systems are considered good models of molecular glasses and we further explore the range of validity of this paradigm using a thermosensitive core-shell particle dispersion to study the aging response of a colloidal glass subsequent to both shear-melting and temperature (concentration)-jump perturbations in the vicinity of the glass transition concentration or temperature. Sequential creep experiments were used to probe the different aging responses of the system. The colloidal glass displays aging behavior after both types of perturbation and our results indicate that this colloidal glass is similar to a molecular glass, in that shift rates are found to be below unity and to decrease towards zero as the glass temperature (or concentration) is approached as temperature increases. However, the kinetics of the aging in the two cases are different indicating that the structural changes induced by the mechanical perturbation are different from those induced by the temperature or concentration jump-similar to findings on mechanical rejuvenation of molecular glasses. We also find differences between the colloidal glass and molecular glasses: In the case of the colloidal glass the structural recovery or equilibration times do not diverge, while the mechanical relaxation times do. On the other hand, for the molecular glass, both times change very rapidly with decreasing temperature, apparently towards a distant point of divergence.